Question 65
If $a, b, c$ are positive real numbers with sum $6$, determine the maximal value of the expression:
$$
S = \sqrt[3]{a^2 + 2bc} + \sqrt[3]{b^2 + 2ca} + \sqrt[3]{c^2 + 2ab}.
$$
$$
S = \sqrt[3]{a^2 + 2bc} + \sqrt[3]{b^2 + 2ca} + \sqrt[3]{c^2 + 2ab}.
$$