$$M$$ and $$N$$ are consecutive integers ($$N = M + 1)$$ such that $$M$$ $$<$$ $$\sqrt{55555 + \sqrt{55555^{2}+ \sqrt{55555^{3} + \sqrt{...}}}}$$ $$<$$ $$N$$. Find the value of $$\frac{M+N}{7}$$.