Find minimum of $a+b$ if $13|a+11b $ and $11|a+13b$ where $a,b>0$.

My attempt :

$13|a+11b \implies 13|a+24b$ . Similarly we get $11|a+24b$. Now $\gcd(11,13)=1$, so, $143|a+24b$.

Therefore $a+24b \geq 143$. 

How to proceed after this?