This is equivalent to,
$\displaystyle x^2\equiv 54 (\bmod 11)$ and $\displaystyle x^2\equiv 54(\bmod 13)$
Which reduces to,
$\displaystyle x^2 \equiv 10 (\bmod 11)$ and $\displaystyle x^2 \equiv 2(\bmod 13)$
This has no solutions.
This is equivalent to,
$\displaystyle x^2\equiv 54 (\bmod 11)$ and $\displaystyle x^2\equiv 54(\bmod 13)$
Which reduces to,
$\displaystyle x^2 \equiv 10 (\bmod 11)$ and $\displaystyle x^2 \equiv 2(\bmod 13)$
This has no solutions.
The question asked for 53, not 54.
And this question is the same as occurred in this thread.