Fun With Calculus-3

Calculus Level 4

\[\large \lim_{x\to \infty}\left [\sqrt[3] {(a+x)(b+x)(c+x)}-x\right ]\] is equal to \(\large \frac{w a+y b+z c} {d}\)\((w,y,z,d\in\)N\()\), then the minimum value of \(w+y+z+d\) is