The production length l(p) of a leading (large z(h)) hadron produced in hadronization of a highly virtual high-p(T) parton is short because of the very intensive vacuum gluon radiation and dissipation of energy at the early stage of the process. Therefore, the main part of nuclear suppression of high-p(T) hadrons produced in heavy ion collisions is related to the survival probability of a colorless dipole propagating through a dense medium. This is subject to color transparency, which leads to a steep rise with p(T) of the nuclear ratio R-AA (p(T)), in good agreement with the recent data from the ALICE experiment at the CERN Large Hadron Collider (LHC). No adjustment, except for the medium density, is made, and the transport coefficient is found to be (q) over cap 0 = 0.8 GeV2/fm. This is close to the value extracted from the analysis of BNL Relativistic Heavy Ion Collider (RHIC) data for J/Psi suppression, but is an order of magnitude smaller than the value found from jet quenching data within the energy loss scenario. Although the present calculations have the status of a postdiction, the mechanism and all formulas have been published, and are applied here with no modification, except for the kinematics. At the same time, p(T) dependence of R-AA at the energy of RHIC is rather flat due to the suppression factor steeply falling with rising x(T), related to the energy conservation constraints. This factor is irrelevant to the LHC data, since x(T) is much smaller.