A combination of measurements sensitive to the $CP$ violation angle $\gamma$ of the Cabibbo-Kobayashi-Maskawa unitarity triangle and to the charm mixing parameters that describe oscillations between $D0$ and $D¯0$ mesons is performed. Results from the charm and beauty sectors, based on data collected with the LHCb detector at CERN's Large Hadron Collider, are combined for the first time. This method provides an improvement on the precision of the charm mixing parameter $y$ by a factor of two with respect to the current world average. The charm mixing parameters are determined to be $x=(0.400-0.053+0.052)\%$ and $y=(0.630-0.030+0.033)\%$. The angle $\gamma$ is found to be $\gamma =(65.4-4.2+3.8)\circ$ and is the most precise determination from a single experiment.