Think before choose... again.

$n$ is an odd integer. Is the following statement true or false?

$\large \sqrt[n]{a} + \sqrt[n]{b} + \sqrt[n]{c} = \sqrt[n]{a + b + c} \iff \dfrac{1}{a^n} + \dfrac{1}{b^n} + \dfrac{1}{c^n} = \dfrac{1}{a^n + b^n + c^n}$

This is part of the series: It's easy, believe me!