  The production of $X(4350)$ in the $\gamma \gamma$ interactions that occur in
proton-proton, proton-nucleus and nucleus-nucleus collisions at the CERN Large
Hadron Collider (LHC) is investigated and predictions for the kinematical
ranges probed by the ALICE and LHCb Collaborations are presented. We focus on
the $\gamma \gamma \rightarrow \phi J/\Psi$ process, which have been measured
by the Belle Collaboration, and present parameter free predictions for the
total cross sections at the LHC energies. Our results demonstrate that the
experimental study of this process is feasible and can be used to confirm or
not the existence of the $X(4350)$ state. Finally, for completeness, we present
predictions for the production of the $X(3915)$ state in the $\gamma \gamma
\rightarrow \omega J/\Psi$ process and show that this exotic state can also be
probed in $\gamma \gamma$ interactions at the LHC.
