Can't think of a good name

For function $f(x)= 1 - x - x^3$ , the values of real $x$ which satisfy the inequality below can be written in the form $(-2,0) \cup (a,\infty)$ .

$\large 1-f(x) - f^{3}(x) > f(1-5x)$

Find the minimum value of $a$ .