Spend a few minutes in *Aerodynamics for Naval Aviators* (despite the title, it's not just for NA's, but is in fact a very good general aerodynamics and propulsion reference) and it is clear that the answer to the question depends solely on the aircraft's powerplant.
In a nutshell, what you will find is this:
1) a normally aspirated piston powerplant loses propulsive efficiency at a rate that negates the true airspeed advantage of flying higher; therefore the maximum range of an airplane with this type of powerplant will be obtained when it is flown at the lowest practical altitude, and at max L/D AOA.
2) turbo- (or super-) charged recip powerplants, or turbine aircraft, will benefit in increased range from climbing to cruise altitude. The *-charged recip should be flown at or near the critical altitude of the powerplant, and the turbine-powered aircraft higher yet...at the tropopause, for jet aircraft, and somewhat lower for turbopropeller aircraft...depending on the efficiencies of the specific engine-propeller combination.
The Breguet equation is to range as the Carnot equation is to efficiency...a theoretical maximum.