$$\left. \begin{array} { l } { 2 y + \frac { 5 } { 3 } = \frac { 26 } { 3 } - y ^ { 3 } } \\ { = } \end{array} \right.$$
$y = \frac{18 ^ {\frac{2}{3}} {(\sqrt[3]{\sqrt{4065} + 63} + \sqrt[3]{63 - \sqrt{4065}})}}{18} \approx 1.568946403$
