One of the most powerful cosmological data sets when it comes to constraining neutrino masses is represented by galaxy power spectrum measurements, Pgg(k). The constraining power of Pgg(k) is however severely limited by uncertainties in the modeling of the scale-dependent galaxy bias b(k). In this work we present a new proof-of-principle for a method to constrain b(k) by using the cross-correlation between the cosmic microwave background (CMB) lensing signal and galaxy maps (C κg) using a simple but theoretically well-motivated parametrization for b(k). We apply the method using C κg measured by cross-correlating Planck lensing maps and the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 11 (DR11) CMASS galaxy sample, and Pgg(k) measured from the BOSS DR12 CMASS sample. We detect a nonzero scale-dependence at moderate significance, which suggests that a proper modeling of b(k) is necessary in order to reduce the impact of nonlinearities and minimize the corresponding systematics. The accomplished increase in constraining power of Pgg(k) is demonstrated by determining a 95% confidence level upper bound on the sum of the three active neutrino masses Mν of Mν<0.19 eV. This limit represents a significant improvement over previous bounds with comparable data sets. Our method will prove especially powerful and important as future large-scale structure surveys will overlap more significantly with the CMB lensing kernel providing a large cross-correlation signal.