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In modified gravity theories, the luminosity distance for gravitational waves (GWs) is in general different from that for electromagnetic signals. This opens the possibility of model-independent tests of GR, by comparing the results from standard candles with those from standard sirens. We illustrate this fact using a nonlocal modification of gravity, that has been shown to fit remarkably well CMB, SNe, BAO and structure formation data. We find that, for rather general reasons, the relative difference between the GW luminosity distance of the modified gravity model and the luminosity distance of \LambdaCDM is larger by one order of magnitude than the relative difference of electromagnetic luminosity distances. This effect would be missed in phenomenological studies that parametrize dark energy using only an equation of state w_{\rm DE}(z. We discuss the prospects for distinguishing nonlocal gravity from \LambdaCDM at third-generation GW detectors such as the Einstein Telescope and we find that, depending on the exact sensitivity, a few tens of standard sirens with measured redshift at z\sim 0.4, or a few hundreds at 1<z<2, could suffice.