Degree of algebraically closed field extensions

Question

Let $\ell$ be a field extension of the field $k$, and let $[\ell : k] = n$ (possibly infinite). Let $\overline{\ell}$ and $\overline{k}$ be algebraic closures of $\ell$ and $k$.

Is it true that $[\overline{\ell} : \overline{k}] \leq n$ ?