  We propose that unconventional superconductivity in hydrated sodium cobaltate
$Na_xCoO_2$ results from an interplay of electronic correlations and
electron-phonon interactions. On the basis of the $t-V$ model plus phonons we
found evidences for a) unconventional superconductivity, b) realistic values of
$T_c$ and c) the dome shape existing near $x \sim 0.35$. This picture is
obtained for $V$ close to the critical Coulomb repulsion $V_c$ which separates
the uniform Fermi liquid from $\sqrt{3} \times \sqrt{3}$ CDW ordered phase.
