Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative$$\frac{2 \left(\frac{2 \operatorname{sign}{\left(x + 1 \right)}}{\sqrt[3]{\left|{x + 1}\right|}} - \frac{3 \left|{x + 1}\right|^{\frac{2}{3}}}{x + 1}\right)}{9 \left(x + 1\right)} = 0$$
Solve this equationSolutions are not found,
maybe, the function has no inflections