  Recent experimental and theoretical studies suggest that the quarkonia
suppression in a thermal QCD medium created at heavy ion collisions is a
complex interplay of various physical processes. In this article we put
together most of these processes in a unified way to calculate the charmonium
survival probability (nuclear modification factor) at energies available at
relativistic heavy ion collider (RHIC) and large hadron collider (LHC)
experiments. We have included shadowing as the dominant cold nuclear matter
(CNM) effect. Further, gluo-dissociation and collision damping has been
included which provide width to the spectral function of charmonia in a thermal
medium and causes the dissociation of charmonium along with usual colour
screening. We include the colour screening using our recently proposed modified
Chu and Matsui model. Furthermore we incorporate the recombination of
uncorrelated charm and anti-charm quark for the regeneration of charmonium over
the entire temporal evolution of QGP medium. Finally we do the feed-down
correction from the excited states to calculate the survival probability of
charmonium. We find that our unified model suitably describes the experimental
nuclear modification data of $J/\psi$ at RHIC and LHC simultaneously.
