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We use the Fundamental Plane (FP) to measure the redshift evolution of the dynamical mass-to-light ratio ($M_{\mathrm{dyn}}/L$) and the dynamical-to-stellar mass ratio ($M_{\mathrm{dyn}}/M_*$). Although conventionally used to study the properties of early-type galaxies, we here obtain stellar kinematic measurements from the Large Early Galaxy Astrophysics Census (LEGA-C) Survey for a sample of $\sim1400$ massive ($\log( M_*/M_\odot) >10.5$) galaxies at $0.6<z<1.0$ that span a wide range in star formation activity. In line with previous studies, we find a strong evolution in $M_{\mathrm{dyn}}/L_g$ with redshift. In contrast, we find only a weak dependence of the mean value of $M_{\mathrm{dyn}}/M_*$ on the specific star formation rate, and a redshift evolution that likely is explained by systematics. Therefore, we demonstrate that star-forming and quiescent galaxies lie on the same, stable mass FP across $0<z<1$, and that the decrease in $M_{\mathrm{dyn}}/L_g$ toward high redshift can be attributed entirely to evolution of the stellar populations. Moreover, we show that the growth of galaxies in size and mass is constrained to occur within the mass FP. Our results imply either minimal structural evolution in massive galaxies since $z\sim1$, or a tight coupling in the evolution of their morphological and dynamical properties, and establish the mass FP as a tool for studying galaxy evolution with low impact from progenitor bias.