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This Letter presents the most precise measurement to date of the matter/antimatter imbalance at midrapidity in Pb-Pb collisions at a center-of-mass energy per nucleon pair sNN−−−√=5.02 TeV. Using the Statistical Hadronization framework, it is possible to obtain the value of the electric charge and baryon chemical potentials, μQ=−0.18±0.90 MeV and μB=0.71±0.45 MeV, with unprecedented precision. A centrality-differential study of the antiparticle-to-particle yield ratios of charged pions, protons, Ω-baryons, and light (hyper)nuclei is performed. These results indicate that the system created in Pb-Pb collisions at the LHC is on average baryon-free and electrically neutral at midrapidity.