I'm trying to solve a question which asks me to find the degree of the splitting field of $x^5 - t$ over $\mathbb{F}_{11}(t)$.
I honestly have no idea where to begin - the only other examples of splitting fields I've done have been over $\mathbb{Q}$ which was very easy to work with.
I saw Degree of a splitting field over $ \mathbb{F}_{4}(t)$ which looks somewhat similar, but the answers there involve Galois groups which I don't think I'm supposed to use because I haven't encountered them in the course yet.
Can anyone offer any help?