Answer
$-4\sqrt[3]{x}+7\sqrt{7}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
3\sqrt{7}-\sqrt[3]{x}+4\sqrt{7}-3\sqrt[3]{x}
\\=
(-\sqrt[3]{x}-3\sqrt[3]{x})+(3\sqrt{7}+4\sqrt{7})
\\=
-4\sqrt[3]{x}+7\sqrt{7}
.\end{array}