• The roots add to the negative of the x coefficient.
• The roots multiply to the constant term.

The given equation, after reducing, is equivalent to this quadratic equation

    6x^2 - 16x + 7 = 0.    (1)


According to Vieta's theorem, if "a" and "b" are the roots of this quadratic equation, then

    a + b =  = ,     (2)

      ab  = .           (3)


Now,   +  = .


The numerator is

    a^3 + b^3 = (a+b)*(a^2 - ab + b^2) = (a+b)*((a^2+2ab+b^2)-3ab) = (a+b)*((a+b)^2-3ab) = (a+b)^3 - 3(a+b)*(ab).


Now replace here  (a+b)  by   8/3  based on  (2)  and replace ab by  7/6  based on (3).

You will get  


    a^3 + b^3 =  -  =  -  =  -  =  = .


Therefore,   =  =  =  = .


ANSWER.   = .