I have the following special function.
$$f(x) = \sum _{i=1}^n \left\{\frac{(x - z_i)_+^2}{1+ 2*z_i+(x - z_i)_+^2}\right\} - \left\{(\frac{x^3}{3} - \frac{(x - z_i)_+^3}{3})\right\} $$
which + means If $z_i$ is bigger than x its equal $z_i - x$ and else it's equal zero.
Also $z_i$ is a vector of value.
How can I find the root of this cubic function?