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We present a non-perturbative computation of inclusive rates of semileptonic decays of heavy mesons from lattice QCD simulations. The calculation is based on the extraction of smeared spectral functions obtained from four-point Euclidean correlation functions computed on configuration ensembles of the JLQCD and ETM collaborations. We compare our results for the inclusive decay rates with analytical predictions from the operator-product expansion, finding a good agreement for the calculation of the inclusive decay rate. This opens the path to the theoretical determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $V_{cb}$ to a level of precision competitive with the present experimental uncertainty.