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

A way to do it. by Gamer)

...." cube thing could be done more easily than it seems. If you ever saw the cube root of 12, 1728, you could think "Wow; if you add the one at the beginning to the ...

THERE TOO MANY ERRORS

IN THIS STATEMENT TO UNDERSTAND WHAT YOU HAD IN MIND...

a Please explain

b In the future- eschew obfuscation

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