The study of charge excitations in cuprate superconductors is an active topic in present days. Recent resonant inelastic x-ray scattering (RIXS) experiments detected low-energy plasmons in electron-doped (e-cuprates) and hole-doped (h-cuprates) cuprates. These plasmon excitations are, in leading order of a $1/N$ approximation, satisfactorily described in the context of the layered $t$-$J$ model with long-range Coulomb interaction. On the basis of this model, and beyond the leading order in $1/N$, the role of plasmons in the electron self-energy and the spectral functions is discussed. As a salient feature, it was found an emergent band (a sharp side band) which was interpreted as the combined effect of correlations and plasmons. The possible role of these findings in ARPES experiments on h- and e-cuprates is also discussed.