What is the smallest positive integer that is the sum of two different pairs of (non-zero, positive) cubes?

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What is the smallest positive integer that is the sum of two different pairs of integers raised to the 4th power? and how did you find it?

In other words what is the smallest x such that:

x = a^4 + b^4 = c^4 + d^4

(where x, a, b, c, and d are all different, non-zero, positive integers)?

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Are you able to determine the answer without looking it up on the internet?

(In reply to

re(2): A way to do it.===> NO WAY by Frank Riddle)

Dear FR,

Thanks for trying to " unobfuscate" me.

Please comment why "...the cube root of 12, 1728, you.." etc

is compatible with " There is not a single error in the statement..".

The issue of 1728 ===>1+728 is clear, believe me.The issue of " the cube root of 12".... much less.

ady