\[\sqrt[3]{- 2\frac{10}{27}} + 8\sqrt[4]{5\frac{1}{16}} = \sqrt[3]{- \frac{64}{27}} + 8\sqrt[4]{\frac{81}{16}} =\]
\[= - \frac{4}{3} + 8 \cdot \frac{3}{2} = - 1\frac{1}{3} + 12 = 10\frac{2}{3}.\]