Don't run out of patience

Algebra Level 5

\[\sum _{r=1} ^n \frac{1}{r(r+1)(r+2)(r+3)} = \dfrac{1}{a} - \dfrac{1}{b(n+1)}+ \dfrac{1}{c(n+2)}- \dfrac{1}{d(n+3)}\]

If the equation above holds true for constants \(a\), \(b\), \(c\) and \(d\), find \(a+b+c+d\).