Sum of first, second, and third powers are all squares

I recently came across this interesting pair of numbers: 345 and 184.
The sum of their first, second, and third powers are all perfect
squares:
345 + 184 = 23^2
345^2 + 184^2 = 391^2
345^3 + 184^3 = 6877^2

Are there any other nontrivial pairs like this, other than multiples
of these pairs?  I did a brute force search up to 46000 and found only
this pair and its multiples.