OMM 2014 Problem 5

Let $a, b, c$ be positive reals such that $a + b + c = 3$ . Prove:

$$\frac{a^2}{a + \sqrt[3]{bc}} + \frac{b^2}{b + \sqrt[3]{ca}} + \frac{c^2}{c + \sqrt[3]{ab}} \geq \frac{3}{2}$$

And determine when equality holds.