The cross section for coherent J/ψ photoproduction accompanied by at least one neutron on one side of the interaction point and no neutron activity on the other side, (X_{n}0_{n}), is measured with the CMS experiment in ultra-peripheral PbPb collisions at (\sqrt{s_{\mathrm{NN}}})=2.76TeV. The analysis is based on a data sample corresponding to an integrated luminosity of 159 μb(^{−1}), collected during the 2011 PbPb run. The (J/ψ) mesons are reconstructed in the dimuon decay channel, while neutrons are detected using zero degree calorimeters. The measured cross section is (dσ_{{{X}{n}}{{0}{n}}}^{coh}/dy(J/ψ)) = 0.36 ± 0.04 (stat) ± 0.04 (syst) mb in the rapidity interval 1.8 < |y| < 2.3. Using a model for the relative rate of coherent photoproduction processes, this (X_{n}0_{n}) measurement gives a total coherent photoproduction cross section of (dσ^{coh}/dy(J/ψ)) = 1.82 ± 0.22 (stat) ± 0.20 (syst) ± 0.19 (theo) mb. The data strongly disfavor the impulse approximation model prediction, indicating that nuclear effects are needed to describe coherent (J/ψ) photoproduction in (γ)+Pb interactions. The data are found to be consistent with the leading twist approximation, which includes nuclear gluon shadowing.