But I don't have a calculator with me!

Algebra Level 2

\[ \LARGE \sqrt[\color{green}3]{\color{brown}5+\color{blue}2\sqrt{\color{fuchsia}{13}}} + \sqrt[\color{green}3]{\color{brown}5-\color{blue}2\sqrt{\color{fuchsia}{13}}} =\ \color{grey} ? \]