Find the smallest positive integer x where 149|(x^2-69^3) $$
\text{Find the smallest positive integer x where 149|}\left( \text{x}^2-69^3 \right) 
$$
I almost do not spot any clue about this question.
It is from PUMaC-CHINA, 2019.8.17

A minute of mental arithmetic via $\sqrt{69^{\large 3}}\equiv 69\sqrt{\color{#90f}{69}}\,$ then negating & pulling out more squares 
$\!\bmod 149\!:\,\  \color{#90f}{69}\equiv -80\equiv \color{#0a0}{-5}\cdot 4^{\large 2}\equiv \color{#0a0}{144}(4^{\large 2})\equiv \color{#0a0}{12^{\large 2}} 4^{\large 2}\equiv 48^{\large 2} $ 
${\rm therefore}\ \ \ \ 69\equiv 48^{\large 2}\,\overset{\large \times\, 69^{\Large 2}}\Longrightarrow\,69^{\large 3}\equiv {\underbrace{(69\cdot 48)}_{\large  23\,\cdot\, \underbrace{3\,\cdot\, 48}_{\LARGE {\bf -}5\ \ }}}^{\large 2}\equiv \color{#c00}{34^{\large 2}}$
