Let $L/K$ be a totally ramified finite radical extension of local fields of characteristic $0$, where $L = K(\sqrt[p^m] a)$ and $p$ is the characteristic of the residue field.
If $v_K(a)=1$, then $X^{p^m}-a$ is an Eisenstein polynomial, $[L:K]=p^m$ and $\sqrt[p^m] a $ is a uniformizer of $L$ satisfying $\mathcal O_L = \mathcal O_K[\sqrt[p^m] a ]$. But if this assumption is not given, I was not able to find a similar statement.
Is it possible to determine a uniformizer or a $\mathcal O_K$-generator of $\mathcal O_L$ in general?