A natural resolution for the Cabibbo angle anomaly and $R_{K^{(*)}}$

We identify a single six-dimensional effective operator $O_{ellell}$ that can account for the Cabibbo angle anomaly naturally, without any tension with the electroweak precision observables. The renormalization group running of $O_{ell ell}$ yields the required new couplings of $W$ and $Z$ bosons in exactly the right proportion. When generated as a result of a $Z$ model, the non-universal leptonic coupling needed for this operator can also contribute to the lepton flavor universality violating $R_{K^{(*)}}$ anomaly, generating the preferred relation $C_9=-C_{10}$ between the Wilson coefficients. We find the region in parameter space of $Z$ mass and couplings that offer a simultaneous solution to both these anomalies, and argue that $O_{ell ell}$ is a unique single operator that can offer such a resolution. Our arguments may also be extended to multi-operator scenarios like $U_1$ vector leptoquark, which is known to address multiple anomalies that violate the lepton flavor universality.