Triple Trouble!

Calculus Level 4

$\displaystyle\int_0^{\infty}\displaystyle\int_0^{\infty}\displaystyle\int_0^{\infty} \dfrac{\ dx \ dy \ dz}{\sqrt{(1+x+y+z)^7}}$

If the above integral can be expressed as $\dfrac{S}{G}$ . Find $\overline{SG}$

$\implies$ S,G are coprime integers

$\implies$ If the answer is 17/15 the you should input 1715.