1           
3√(a) + 3√(b) +  3√(c)

Use these formulas:
1) (a+b+c)(a²+b²+c²-ab-bc-ca)=a³+b³+c³-3abc
2) (x-y)(x²+xy+y²)=x³-y³

After using (1) denominator will be
(a+b+c-3(abc)^(1/3))

Now use (2) considering a+b+c = x and 3(abc)^(1/3) = y

The final denominator will be (a+b+c)³ - 27(abc)