Well the answer is n=8
I got this from the graph
https://www.desmos.com/calculator/ncyzikps9l
I also got it from our web2.0calc
$${\frac{{{\mathtt{n}}}^{{\mathtt{3}}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{{\mathtt{n}}}^{{\mathtt{2}}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{n}}}{{\mathtt{3}}}}{\mathtt{\,-\,}}{\mathtt{120}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{n}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{239}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{11}}\right)}{{\mathtt{2}}}}\\
{\mathtt{n}} = {\frac{\left({\sqrt{{\mathtt{239}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{11}}\right)}{{\mathtt{2}}}}\\
{\mathtt{n}} = {\mathtt{8}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{n}} = {\mathtt{\,-\,}}\left({\frac{{\mathtt{11}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7.729\: \!812\: \!416\: \!869\: \!953}}{i}\right)\\
{\mathtt{n}} = {\mathtt{\,-\,}}{\frac{{\mathtt{11}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7.729\: \!812\: \!416\: \!869\: \!953}}{i}\\
{\mathtt{n}} = {\mathtt{8}}\\
\end{array} \right\}$$
Well the answer is n=8
I got this from the graph
https://www.desmos.com/calculator/ncyzikps9l
I also got it from our web2.0calc
$${\frac{{{\mathtt{n}}}^{{\mathtt{3}}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{{\mathtt{n}}}^{{\mathtt{2}}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{n}}}{{\mathtt{3}}}}{\mathtt{\,-\,}}{\mathtt{120}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{n}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{239}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{11}}\right)}{{\mathtt{2}}}}\\
{\mathtt{n}} = {\frac{\left({\sqrt{{\mathtt{239}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{11}}\right)}{{\mathtt{2}}}}\\
{\mathtt{n}} = {\mathtt{8}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{n}} = {\mathtt{\,-\,}}\left({\frac{{\mathtt{11}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7.729\: \!812\: \!416\: \!869\: \!953}}{i}\right)\\
{\mathtt{n}} = {\mathtt{\,-\,}}{\frac{{\mathtt{11}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7.729\: \!812\: \!416\: \!869\: \!953}}{i}\\
{\mathtt{n}} = {\mathtt{8}}\\
\end{array} \right\}$$