fake proofs - imaginary number $i$ equals $-6/3.4641$?

$$-4^3 = -64$$
so the third root of $-64$ should be $-4$ than.
$$\sqrt[3]{-64} = -4$$
But if you calculate the third root of -64
with WolframAlpha( http://www.wolframalpha.com/input/?i=third+root+of+-64 )
you get a complex number with an imaginary part of $$3.4641016151 i$$ and a real part of $$2$$

so if the third root of $4-64$ equals $-4$ AND $2 + 3.46410162 i$ (which i know is a bit foolish) than you could actually reform it like this
$$
\sqrt[3]{-64} \approx 2 + 3.46410162 i | -2$$
$$
\sqrt[3]{-64} -2 \approx -6 \approx 3.46410162 i |/3.46410162$$
$$
\frac{\sqrt[3]{-64} -2}{3.46410162} ≈ \frac{-6}{3.46410162} ≈ i$$

and this have to be totally wrong, so my question is, where exactly is the mistake?