The cross section for coherent J/psi 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[NN]) = 2.76 TeV. The analysis is based on a data sample corresponding to an integrated luminosity of 159 inverse microbarns, collected during the 2011 PbPb run. The J/psi mesons are reconstructed in the dimuon decay channel, while neutrons are detected using zero degree calorimeters. The measured cross section is dsigma[coh,X[n]0[n]] / dy(J/psi) = 0.36 +/- 0.04 (stat) +/- 0.04 (syst) mb in the rapidity interval 1.8 < abs(y) < 2.3. Using a model for the relative rate of coherent photoproduction processes, this X[z,n,z] measurement gives a total coherent photoproduction cross section of dsigma[coh] / dy(J/psi) = 1.82 +/- 0.22 (stat) +/- 0.20 (syst) +/- 0.19 (theo) mb. The data strongly disfavour the impulse approximation model prediction, indicating that nuclear effects are needed to describe coherent J/psi photoproduction in gamma + Pb interactions. The data are found to be consistent with the leading twist approximation, which includes nuclear gluon shadowing.