the construction of a segment

[Albert]

given :AB=1 and ,CD=a, EF=b

Can you construct a segment with length =$\dfrac {1}{a^3}+\dfrac {1}{b^3}$

 

[Albert]

given :AB=1 and ,CD=a, EF=b

Can you construct a segment with length =$\dfrac {1}{a^3}+\dfrac {1}{b^3}$

Spoiler

the diagrams are not scaled