\[6\sqrt[3]{- \frac{1}{8}} + 20\sqrt[4]{5\frac{1}{16}} = 6 \cdot \left( - \frac{1}{2} \right) + 20\sqrt[4]{\frac{81}{16}} =\]
\[= - 3 + 20 \cdot \frac{3}{2} = - 3 + 30 = 27.\]