To simplify this inequality, we first expand the cubed terms on the left side:

(x-1)³ = x³ - 3x² + 3x - 1
(x+1)³ = x³ + 3x² + 3x + 1

Therefore, the left side of the inequality becomes:

(x³ - 3x² + 3x - 1) - (x³ + 3x² + 3x + 1)
= x³ - 3x² + 3x - 1 - x³ - 3x² - 3x - 1
= -6x²

Now, the inequality becomes:

-6x² ≤ x - 6x²

By adding 6x² to both sides:

0 ≤ x

Therefore, the solution to the inequality is x ≥ 0.