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.
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