Hardy-Ramanujan to 4

If $635,318,657 = m^4 + n^4 = p^4 + q^4$ , where $m$ , $n$ , $p$ , and $q$ are distinct positive integers.

What is the value of $|(p+q)-(m+n)|$ ?

Note that $|\cdot|$ denotes the absolute value function , a positive integer answer expected.