Let $P(x)=x^3+x^2+c$ a polynomial where $c$ is a real number. Then there is a finite interval $I$ such that, $P(x)$ has more than one real root if and only if $c$ is in $I$. If the length of $I$ can be represented as a number of the form $\frac{a}{b},$ where $a$ and $b$ are coprimes, then find $a+b.$