The mixing of $B_{s/d}$ and $\overline{B}_{s/d}$ mesons constitutes a FCNC process and is therefore very sensitive to new physics effects and has the potential to severely constrain models that could explain the current flavour anomalies. We present SM predictions for the mixing observables based on a sum rule determination of the required hadronic matrix elements of the full basis of dimension-six operators, which is a competitive alternative to lattice simulations. Results for the effects of a non-zero strange-quark mass in $B_s$ mixing are shown for the first time. The reliability of the heavy-quark expansion and sum rule results is demonstrated by considering lifetime ratios of $B$ and $D$ mesons where we find very good agreement with the experimental averages.