Cross sections for the coherent photoproduction of ρ⁰ vector mesons in ultra-peripheral Pb-Pb collisions at sNN = 5.02 TeV are reported. The measurements, which rely on the π⁺π⁻ decay channel, are presented in three regions of rapidity covering the range |y| < 0.8. For each rapidity interval, cross sections are shown for different nuclear-breakup classes defined according to the presence of neutrons measured in the zero-degree calorimeters. The results are compared with predictions based on different models of nuclear shadowing. Finally, the observation of a coherently produced resonance-like structure with a mass around 1.7 GeV/c² and a width of about 140 MeV/c² is reported and compared with similar observations from other experiments. [Figure not available: see fulltext.]