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=2.76 TeV . 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 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.