Find all values of $x$ such that
\[
\begin{vmatrix} 1 & 1 & 1 \\ x & 7 & -2 \\ x^3 & 343 & -8 \end{vmatrix}
= 0.\]Enter your values separated by commas.  For example, if you think the possible values are 4, 5, and 6, then enter you answer as "4,5,6".
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find all values of $x$ such that
\[
\begin{vmatrix} 1 & 1 & 1 \\ x & 7 & -2 \\ x^3 & 343 & -8 \end{vmatrix}
= 0.\]Enter your values separated by commas.  For example, if you think the possible values are 4, 5, and 6, then enter you answer as "4,5,6".
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
7, -2, \text{ and } -5
Find all values of $x$ such that
\[
\begin{vmatrix} 1 & 1 & 1 \\ x & 7 & -2 \\ x^3 & 343 & -8 \end{vmatrix}
= 0.\]Enter your values separated by commas.  For example, if you think the possible values are 4, 5, and 6, then enter you answer as "4,5,6".
train