Elements of high order in finite fields specified by binomials

Let $F_q$ be a field with $q$ elements, where is power of prime number $p\geq 5$. For any integer $m\geq 2$ and $a\in F_q^*$ such that the polynomial $x^m-a$ irreducible in $F_q[x]$, we combine two different methods to explicitly construct elements high order $F_q[x]/\langle x^m-a\rangle$. Namely, find multiplicative at least $5^{\sqrt[3]{m/2}}$, which better than previously obtained bound for family extension fields.