[tex](8x^3-9)^3=5832[/tex]
Cube root each side.
∛5832 = 18. You can prime factorize to find this.
[tex]8x^3-9=18[/tex]
Add 9 to each side.
[tex]8x^3=27[/tex]
Divide by 8.
[tex]x^3=\frac{27}8[/tex]
Cube root each side.
[tex]\boxed{x=\frac{3}2}[/tex]
Note that radicals with an odd index (cube roots, 5th, 7th, etc.) don't leave a plus-minus...If there's an even number all of the negatives cancel, but if it's odd, it won't, just as with exponents.
