Perfect powers in polynomial power sums

We prove that a non-degenerate simple linear recurrence sequence $(G_n(x))_{n=0}^{\infty}$ of polynomials satisfying some further conditions cannot contain arbitrary large powers of polynomials if the order of the sequence is at least two. In other words we will show that for $m$ large enough there is no polynomial $h(x)$ of degree $\geq 2$ such that $(h(x))^m$ is an element of $(G_n(x))_{n=0}^{\infty}$. The bound for $m$ depends here only on the sequence $(G_n(x))_{n=0}^{\infty}$. In the binary case we prove even more. We show that then there is a bound $C$ on the index $n$ of the sequence $(G_n(x))_{n=0}^{\infty}$ such that only elements with index $n \leq C$ can be a proper power.