#### Answer

$6\sqrt[]{7}+\sqrt[4]{11}$

#### Work Step by Step

By combining like radicals, the given expression, $
5\sqrt[]{7}-8\sqrt[4]{11}+\sqrt[]{7}+9\sqrt[4]{11}
,$ simplifies to
\begin{array}{l}\require{cancel}
(5\sqrt[]{7}+\sqrt[]{7})+(-8\sqrt[4]{11}+9\sqrt[4]{11})
\\\\=
6\sqrt[]{7}+\sqrt[4]{11}
.\end{array}