  The diffractive vector meson photoproduction with hadron dissociation in
coherent hadron-hadron interactions at LHC energies is studied assuming that
the color singlet $t$-channel exchange carries large momentum transfer. We
estimate the rapidity distribution and total cross section for the processes
$pp \rightarrow p V X$ and $PbPb \rightarrow Pb V X$ ($V = \rho$ or $\Upsilon$)
considering the non-forward solution of the BFKL equation at high energy and
large momentum transfer. Our results indicate that the experimental
identification of these processes can be feasible at the LHC.
