The wing will create best glide at a certain fixed angle of attack. As long as you don't change the wing profile, this angle of attack is a fixed value.
That is correct at lower mach number where compressibility effect is low (approx Mach <0.4 )
At high Mach number,, mentioned AoA also changes, therefore for same weight as fly higher altitude, (Cl /Cd)max (=(L/D) max for certain weight) Green dot speed increases
Note for an Airliner wing profile (Cl /Cd)max AoA is aproximately 4 degree at low mach number