Let $1+a^4+b^4=c^4+d^4$ such that $a$,$b$,$c$ and $d$ are all positive Integers.

How to find Infinitely many solutions ?

By computer search up to $a$,$b$,$c$,$d$ $<3600$ , I found two solutions :

$1+25^4+42^4=17^4+43^4$

$1+405^4+1786^4=253^4+1787^4$