解析：令(a+√3b)^3=54+30√3
即a^3+3√3a^2b+9ab^2+3√3b^3=54+30√3
a^3+9ab^2+3√3(a^2b+b^3)=54+30√3
∴a^3+9ab^2=54,a^2b+b^3=10
解得a=3,b=1
∴(3+√3)^3=54+30√3
同理(3-√3)^3=54-30√3,
（54+30√3）^(1/3)+(54-30√3)^(1/3)
=[(3+√3)^3]^(1/3)+[(3-√3)^3]^(1/3)
=(3+√3)+(3-√3)
=6