The maxi-range is the angle of attack where you get the maximum distance for a unit of fuel (the best distance for fuel consumption). Cd = Ch/ Vs where CH is consumption per hour and Vs = ground speed.
It is easy to demonstrate that the MR is obtain for the best Cl/Cd ratio (Piston engines) and best ratio: square root of Cl divided by Cd for turbine engine.
But the cost per hour of flight is not only depending upon fuel. If you accept to increase the fuel consumption by 1% the speed will be increased by 3 or 4 %. This is the Long Range: an accepted increase of 1% in Cd in front of the MR giving an increase in speed of around 3%.
This was with no wind....
After you have to take into account the wind
Regards.