(1+sqrt(5))^3=1+3sqrt(5)+3*5+5sqrt(5)=16+8sqrt(5)=8(2+sqrt(5)).
So cuberoot(2+sqrt(5))=(1+sqrt(5))/2.
(1-sqrt(5))^3=1-3sqrt(5)+3*5-5sqrt(5)=16-8sqrt(5)=8(2-sqrt(5)).
So cuberoot(2-sqrt(5))=(1-sqrt(5))/2.
Therefore cuberoot(2+sqrt(5))+cuberoot(2-sqrt(5))=(1+sqrt(5)+1-sqrt(5))/2=1.
[The cube roots of 2+sqrt(5) are related to the Golden Ratio which arises from the solution of x=1/(1+x).]