How to solve this nice math radical Exponential algebra problem | Olympiad Question | x=?

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a=³√(x+49);b=³√(x-49);
a-b=2; a³-b³=49+49=98;
(a-b)³=a³-b³-3ab(a-b);
2³=98-3ab(2);=>ab=15;
a-b=2; =>(b+2)b=15;
b²+2b-15=0;
(b+5)(b-3)=0; b=-5 or 3;
b³=-125 or 27=x-49;
x= -76 or 76; verified✓

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