Several major points to be considered in isolation, and then merged.
.1. The optimum speed for maximum range cruise (MRC) at ANY altitude is found at the tangent of a line drawn from the origin 0/0 to the Total Drag / Thrust Required Vs TAS Curve. As weight reduces, the total drag curve moves closer to the 0/0 origin in both axes, i.e. Downwards and to the Left.
At Lower altitudes where MRC speed is below Mcrit, Maximum Range EAS will be constant for a given weight, regardless of altitude, thus Maximum Range CAS for a given weight increases with altitude. As weight reduces, EAS, and thus CAS, reduce for a fixed or increasing altitude. AoA is the dominant factor. For a given weight, Thrust Required remains constant with increasing altitude.
At Higher altitudes where MRC speed is above Mcrit, the Drag / Thrust Required Vs TAS Curve point of tangency is in the region where Drag / Thrust Required rises more steeply due to wave drag, and is therefore at a lower EAS, and defined by Mach No. As altitude increases, MRC Mach No. INCREASES, the speed schedule is no longer constant. AoA is no longer the dominant factor, wave drag becomes much more prominent in assessing the MRC speed schedule as altitude increases above the level at which MRC EAS = Mcrit. For a given weight, Thrust Required increases with increasing altitude.This is the region where Jet aeroplanes spend most of their time.
.2. Where a Head or Tail Wind component is introduced, the Total Drag Curve moves laterally to the Left or Right, depending upon the wind component. A Tail Wind effectively moves the 0/0 origin to the Left, creating a lower point of tangency, and a LOWER MRC speed, whether it be defined as EAS or Mach No. A Head Wind effectively moves the 0/0 origin to the Right, creating a higher point of tangency and a HIGHER MRC speed, whether it be defined as EAS or Mach No.
Thus far, we have seen the relationship between Thrust required to produce the MRC speed schedule. Fuel Flow is required to produce Thrust.
.3. Jet engines have one particular speed (be it N1, N2, N3, or a combination of all of them) where Thrust Specific Fuel Consumption (TSFC) is at it's optimum, i.e. the engine speed where the required thrust is generated for the least Fuel Flow. This speed varies but is usually in the vicinity of 90-93%, NOT maximum. Above and below the optimum TSFC engine speed, it costs more in fuel to produce the requisite thrust. Maximum Range Cruise at low levels requires the same thrust as at somewhat higher levels, but at an engine speed somewhat below optimum TSFC speed, and therefore fuel-inefficient. As we climb higher, engine speed must increase to produce the same thrust for MRC, but at an engine speed approaching optimum TSFC speed. When MRC speed is achieved at an engine speed which offers the optimum TSFC, the aircraft is at OPTIMUM ALTITUDE. Any further climb above this level requires engine speed to increase above optimum TSFC R.P.M., and fuel consumed per mile increases again, just as it did at lower levels. Cruise above OPTIMUM LEVEL will often be at LOWER Fuel Flows, looks good, but it is the fuel consumed per mile that matters, not Fuel Flow in isolation, as would be the case for holding.
As mentioned earlier, when cruising at levels where MRC is defined by Mach No., for a given weight, Thrust Required increases with increasing altitude, but, up to the Optimum Level, TSFC efficiency improves at a greater rate than does drag rise.
That's the short answer, there's much more.
Good luck with CX,
Old Smokey