the splitting field of $x^3-3$ over $\mathbb{Q}_3$

Question

I would like to know the splitting field of $x^3-3$ over $\mathbb{Q}_3$.

・$x^3-3$ has no solution in $\mathbb{Q}_3$ by hensel lemma.

・I don't know how to find $3$ roots in algebraic closure of $\mathbb{Q}_3$.

・This must be subgroup of symmetric group $S_3$ because change of roots are subgroup of $S_3$.

Thank you in advance.