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Incoherent J/psi photoproduction in heavy ion ultraperipheral collisions (UPCs) provides a sensitive probe of localized, fluctuating gluonic structures within heavy nuclei. This Letter reports the first measurement of the photon-nucleon center-of-mass energy (W-gamma N) dependence of this process in PbPb UPCs at a nucleon-nucleon center-of-mass energy of 5.02 TeV, using 1.52 nb(-1) of data recorded by the CMS experiment. The measurement covers a wide W-gamma N range of approximate to 40-400 GeV, probing gluons carrying a fraction x of nucleon momentum down to an unexplored regime of 6.5 x 10(-5). Compared to baseline predictions neglecting nuclear effects, the measured cross sections exhibit significantly greater suppression at lower x. Additionally, the ratio of incoherent to coherent photoproduction is found to be constant across the probed W-gamma N and x range, disfavoring the establishment of the black disk limit. This Letter provides critical insights into the x-dependent evolution of fluctuating gluonic structures within nuclei and calls for further advancements in theoretical models incorporating nuclear shadowing and gluon saturation.