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 s NN =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 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.