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We study the stress tensor multiplet four-point function in the 6d maximallysupersymmetric $(2,0)$ $A_{N-1}$ and $D_N$ theories, which have no Lagrangiandescription, but in the large $N$ limit are holographically dual to weaklycoupled M-theory on $AdS_7\times S^4$ and $AdS_7\times S^4/\mathbb{Z}_2$,respectively. We use the analytic bootstrap to compute the 1-loop correction tothis holographic correlator coming from Witten diagrams with supergravity $R$and the first higher derivative correction $R^4$ vertices, which is the first1-loop correction computed for a non-Lagrangian theory. We then take the flatspace limit and find precise agreement with the corresponding terms in the 11dM-theory S-matrix, some of which we compute for the first time usingtwo-particle unitarity cuts.

6d (2,0) and M-theory at 1-loop