Splitting field of $x^p − x + t$ not solvable over F

Question

Given $p$ is a prime, $k$ is an algebraically closed field of characteristic $p$. and $F = k(t)$, where $t$ is a variable, let $L$ be the splitting field of $x^p − x + t$ over $F$. Then it can be shown that $L$ is not solvable over $F$. Does anyone know where to find a proof or how to prove. I cannot seem to find the proof even though it seems like a standard result in Galois Theory~