The interval in which the function f given by $f(x)=x^3+\frac{1}{x^3}, x \neq 0$ is increasing:

$(-\infty, \infty)$ $(-1,0) \cup(0,1)$ $(-\infty,-1) \cup(1, \infty)$  $(-1,1)$

$(-\infty,-1) \cup(1, \infty)$

The correct answer is Option (3) - $(-\infty,-1) \cup(1, \infty)$