The helicity dependence of the $\ensuremath{\gamma}p\ensuremath{\rightarrow}n{\ensuremath{\pi}}^{+}$ reaction has been measured for the first time in the photon energy range from 450 to 790 MeV. The experiment, performed at the Mainz Microtron (MAMI), used a $4\ensuremath{\pi}$-detector system, a circularly polarized, tagged photon beam, and a longitudinally polarized frozen-spin target. Although these polarized data are mainly sensitive to mechanisms involving the ${D}_{13}(1520)$ resonance, a cusp structure at the \ensuremath{\eta} production threshold can be clearly observed. These data are significantly different from the predictions of the existing multipole analyses and are used to determine the helicity amplitudes of the ${D}_{13}(1520)$ and ${S}_{11}(1535)$ resonances with improved accuracy.