I will present a purely physical M-theoretic derivation of a 5d and 6d AGT correspondence for arbitrary compact Lie groups and ALE spaces, as well as identities between the ordinary, q-deformed and elliptic affine W-algebras associated with the 4d, 5d and 6d AGT correspondences which underlie a quantum geometric Langlands duality and its higher analogs first defined by Frenkel-Reshetikhin. As an offshoot, I will elucidate the sought-after connection between the gauge-theoretic realization of the geometric Langlands correspondence by Kapustin-Witten and its algebraic CFT formulation by Beilinson-Drinfeld, where Wilson and 't Hooft/Hecke line operators in gauge theory can be understood as monodromy loop operators in CFT, for example. I will also explain why the higher analogs of the geometric Langlands correspondence for simply-laced Lie (Kac-Moody) groups G (KMG), ought to relate the quantization of circle (elliptic)-valued G Hitchin systems to circle (elliptic)-valued LG-bundles over a complex curve on one hand, and the transfer matrices of a G (KMG)-type XXZ/XYZ spin chain on the other, where LG is the Langlands dual of G.