$x_1, x_2, x_3, x_4, x_5, x_6$ are six integers such that $x_6>x_5>x_4>x_3>x_2>x_1 \ge 1$. If the maximum possible value of $ \frac {1}{lcm(x_1, x_2)}+\frac {1}{lcm(x_2, x_3)}+\frac {1}{lcm(x_3, x_4)}+ \frac {1}{lcm(x_4, x_5)}+\frac {1}{lcm(x_5, x_6)}$ can be expressed as $\frac {p}{q}$, where $p, q$ are coprimes, find $p+q$.