The 4th Quite Challenging Number Game

Number Theory Level pending

Tired? ....How many 6-digit numbers satisfy:

\(\overline { abcdef } ={ a }^{ 6 }+{ b }^{ 6 }+{ c }^{ 6 }+{ d }^{ 6 }+{ e }^{ 6 }+{ f }^{ 6 }\)

Surprisingly, there's only one number. So...

Find \(\\ a+b+c+d+e+f\\\) .

This is one of my problems in Game Of Numbers.

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