Both Max Endurance and Max Range are highly dependant upon Fuel Flow. There is a direct relationship between Fuel Flow and Power for a propeller aircraft, and between Fuel Flow and Thrust for a jet aircraft.
I don't know how much complexity it is appropriate to add, but the idea that power is dependent only on fuel consumption is an approximation, at least for a piston engine. Such engines are usually more efficient for high power delivery. Add in the efficiency of the propeller, and I believe there can be small but significant variations in brake specific fuel consumption with speed.
I say
significant because we're finding the minimum of a curve, where the curve is by definition not very steep, so fairly large speed changes cause only small changes in drag. In the same way that the best rate of climb speed is usually substantially above the min sink speed because power available increases with speed, so the best range speed may be considerably higher than min drag, and best endurance may be higher than min power required.
(I presume that there is a similar effect with jets in that their TSFC is better at
lower thrusts. For example
this page claims to derive from Shevell a TSFC that increases substantially with Mach no. Thus best endurance might actually be below minimum drag speed.)