Error using split within an equation

Question

I am getting multiple errors for using split within an equation. I use this command in a number of other places throughout my LaTeX document, but there is one case in which many errors are given saying either:

missing } inserted, \end{split}
missing \right, inserted \end{split}
extra }, or forgotten \right \end{split}

etc..

There is 12 total errors, some of which repeat, all for this one \end{split} occasion.

MWE:

\documentclass{article}
\usepackage{amsmath}

\begin{document}


\begin{equation}
\begin{split}
\label{eq:FullRate}
        W_{full} = \dfrac{2\omega}{9\pi}\left(\dfrac{\sqrt{1+\gamma^2}}{\gamma}\dfrac{m_e\omega}{\hbar}\right)^{3/2}Q\left(\gamma,\dfrac{E_g^*}{\hbar\omega}\right)\:\times\:exp\left\lbrace-\pi\left(\dfrac{E_g^*}{\hbar\omega}+1\right) \\ \times\:\left[K\left(\dfrac{\gamma}{\sqrt{1+\gamma^2}}\right)-E\left(\dfrac{\gamma}{\sqrt{1+\gamma^2}}\right)\right]/E\left(\dfrac{1}{\sqrt{1+\gamma^2}}\right)\right\rbrace
\end{split}
\end{equation}

\end{document}

I apologize for the lengthy equation. Everything compiles normally without the split command inserted. Any ideas why this is causing an error? I've looked through it a hundred times trying to figure out if I left something out but everything seems to be in the right place.

Thank you for any and all help!