(7x-2)^1/3 + (7x+5)^1/3 = 3
=> [(7^1/3)^3)(x^1/3)^3 - (2^1/3)^3)] + [(7^1/3)^3(x^1/3)^3 + (5^1/3)^3) = 3^3
=> [(7)(x) - 2] + [(7)(x) +5] = 27
=> 7x - 2 + 7x + 5 = 27
=> 14x + 3 = 27
=> 14x = 27 - 3
=> 14x = 24
=> x = 24/14
=> x = 12/7
Now let's check the answer:
[7(12/7) - 2]^1/3 + [7(12/7) + 5]^1/3 = 3
=> (12-2)^1/3 + (12+5)^1/3 = 3
=> [(10)^1/3]^3 + [(17)^1/3]^3 = 3^3
=> 10 + 17 = 27
=> 27 = 27
There you go
