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We apply it to the simplest large N duality between the pure Chern-Simons theory and the topological string on the resolved conifold, and obtain a simple integral formula for the free energy. Expanding this integral representation around the large radius point at finite string coupling g(s), we find that it includes not only the M-theoretic resummation a la Gopakumar and Vafa, but also a non-perturbative correction in g(s). Remarkably, the obtained non-perturbative correction is in perfect agreement with a proposal for membrane instanton corrections in arXiv: 1306.1734. 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