We report the properties of precision time structures of cosmic nuclei He, Li, Be, B, C, N, and O fluxes over an 11-year solar cycle from May 2011 to November 2022 in the rigidity range from 1.92 to 60.3 GV. The nuclei fluxes show similar but not identical time variations with amplitudes decreasing with increasing rigidity. In particular, below 3.64 GV the Li, Be, and B fluxes, and below 2.15 GV the C, N, and O fluxes, are significantly less affected by solar modulation than the He flux. We observe that these differences in solar modulation are linearly correlated with the differences in the spectral indices of the cosmic nuclei fluxes. This shows, in a model-independent way, that solar modulation of galactic cosmic nuclei depends on their spectral shape. In addition, solar modulation differences due to nuclei velocity dependence on the mass-to-charge ratio (A/Z) are not observed.