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, Xn0n, is measured with the CMS experiment in ultra-peripheral PbPb collisions at sNN=2.76TeV. The analysis is based on a data sample corresponding to an integrated luminosity of 159μb−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 dσXn0ncoh/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 Xn0n measurement gives a total coherent photoproduction cross section of dσcoh/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.