Permutation conjecture for a trinomial over fields of characteristic two

Let $n=2m$ be a positive integer, and let $f(x)$ be the trinomial defined by equation (1) in the source over ${\mathbb F}_{2^{2m}}$. A pair $(s,t)$ specifies the exponents in this trinomial. Permutation conjecture. If

$$\gcd(m,5)=1\quad\text{and}\quad (s,t)=\left(\frac{4}{11},\frac{10}{11}\right),$$

then $f(x)$ is a permutation polynomial over ${\mathbb F}_{2^{2m}}$. The paper proves this conjecture by analyzing the quadratic factors of an eleventh-degree polynomial over ${\mathbb F}_{2^n}$, so the claim is solved.