We present cosmological upper limits on the sum of active neutrino masses using large-scale power spectrum data from the WiggleZ Dark Energy Survey and from the Sloan Digital Sky Survey - Data Release 7 (SDSS-DR7) sample of Luminous Red Galaxies (LRG). Combining measurements on the Cosmic Microwave Background temperature and polarisation anisotropies by the Planck satellite together with WiggleZ power spectrum results in a neutrino mass bound of 0.37 eV at 95% C.L., while replacing WiggleZ by the SDSS-DR7 LRG power spectrum, the 95% C.L. bound on the sum of neutrino masses is 0.38 eV. Adding Baryon Acoustic Oscillation (BAO) distance scale measurements, the neutrino mass upper limits greatly improve, since BAO data break degeneracies in parameter space. Within a ΛCDM model, we find an upper limit of 0.13 eV (0.14 eV) at 95% C.L., when using SDSS-DR7 LRG (WiggleZ) together with BAO and Planck. The addition of BAO data makes the neutrino mass upper limit robust, showing only a weak dependence on the power spectrum used. We also quantify the dependence of neutrino mass limit reported here on the CMB lensing information. The tighter upper limit (0.13 eV) obtained with SDSS-DR7 LRG is very close to that recently obtained using Lyman-alpha clustering data, yet uses a completely different probe and redshift range, further supporting the robustness of the constraint. This constraint puts under some pressure the inverted mass hierarchy and favours the normal hierarchy.