We study the hadron spectra in central AA collisions at RHIC and LHC in a broad pT-range. We cover the low-pT spectra using boost-invariant hydrodynamics with initial energy and net baryon number densities from the pQCD+saturation model [1]. The high-pT spectra are computed using factorized pQCD cross sections, nuclear PDFs and fragmentation functions, and quenching weights for energy losses of high-pT partons in the QGP [2]. Constrained by the RHIC data, we make a prediction for the low- and high-pT hadron spectra, multiplicities and pbar/p ratio in 5% most central Pb+Pb collisions at the LHC. We recognize a rather narrow intermediate pT-range where both the hydro and the pQCD contributions are important. Our results suggest a wider pT-region of applicability for hydrodynamical models at the LHC than at RHIC. [1] K.J. Eskola, et al. Phys. Lett. B566 (2003) 187 [hep-ph/0206230]. [2] K.J. Eskola, et al. Nucl. Phys. A747 (2005) 511 [hep-ph/0406319].