Chapter 7 - Section 7.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set - Page 438: 13

$\dfrac{\sqrt[3]{11}}{3}$

Using the properties of radicals, then, \begin{array}{l} \sqrt[3]{\dfrac{11}{8}}-\dfrac{\sqrt[3]{11}}{6} \\\\= \dfrac{\sqrt[3]{11}}{2}-\dfrac{\sqrt[3]{11}}{6} \\\\= \dfrac{3(\sqrt[3]{11})-\sqrt[3]{11}}{6} \\\\= \dfrac{3\sqrt[3]{11}-\sqrt[3]{11}}{6} \\\\= \dfrac{2\sqrt[3]{11}}{6} \\\\= \dfrac{\sqrt[3]{11}}{3} .\end{array}