We argue that the process gamma+A-->J/psi+"gap"+X at large momentum transfer q(2) provides a quick and effective way to test the onset of a novel perturbative QCD regime of strong absorption for the interaction of small dipoles at the collider energies. We find that already the first heavy-ion run at the LHC will allow one to study this reaction with sufficient statistics via ultraperipheral collisions, hence probing the interaction of qq dipoles of sizes approximately 0.2 fm with nuclear media down to x approximately 10(-5).