Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic

Let $M$ be a field of positive characteristic $p>0$ such that $C$, the closure of a finite field in $M$, has an extension of degree $p$. Let $L$ be a field finitely generated over $C$ and such that $M$ and $L$ are linearly disjoint over $C$. Then Hilbert's Tenth problem is not decidable over $ML$.