Find the asymptotes of $f:\mathbb{R}\to \mathbb{R},f(x)=\sqrt[3]{{e}^{x}-{e}^{2x}+{e}^{4x}{\mathrm{ln}}^{2}(1+{e}^{-x})}.$

I found that y=0 is an asymptote when $x\to -\mathrm{\infty}$, but how do I calculate $\underset{x\to \mathrm{\infty}}{lim}f(x)$ ?