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 $a+b+c+d$ .