Experimental heat-transfer measurements published in the literature seem to be contradictory, some showing a transition of the Nu(Ra) behaviour at Ra≈10^11, some showing a delayed transition at higher Ra, or no transition at all. The physical origin of this discrepancy remains elusive, but is hypothesized to be a signature of the multiple possible flow configurations for a given set of control parameters, as well as the sub-critical nature of the transition to the ultimate regime. New experimental and numerical heat-flux and velocity measurements, both reaching Ra up to 10^12, are reported on a wide range of operating conditions, with either smooth boundaries, or mixed smooth-rough boundaries. Experiments are run in water or fluorocarbon, and aspect ratios 1 or 2. Numerical simulations implement the Boussinesq equations in a closed rectangular cavity with a Prandtl number 4.4, close to the experimental setup, also with smooth boundaries, or mixed smooth-rough boundaries. In the new measurements in the rough part of the cell, the Nusselt number is compatible with a Ra^(1/2) scaling (with logarithmic corrections), hinting a purely inertial regime. In contrast to the Nu v Ra relationship, we evidence that these seemingly different regimes can be reconciled: the heat-flux, expressed as the flux Rayleigh number, RaNu, recovers a universal scaling with Reynolds number, which collapses all data, both our own and those in the literature, once a universal critical Reynolds number is exceeded. This universal collapse can be related to the universal dissipation anomaly, observed in many turbulent flows.