It is hard to compose

$f\left( f\left( f\left( x \right) -2{ x }^{ 3 } \right) \right) \ge f\left( f\left( 2{ x }^{ 3 }-f\left( x \right) \right) \right)$

Let $f\left( x \right) =2{ x }^{ 3 }-21{ x }^{ 2 }+78{ x }+24$ . Find the number of natural numbers in the solution set of $x$ satisfying the inequality above.