Missed it by that much!

Let $l$ be the secant line connecting the points on the graph of $f(x)=x^2$ when $x=n$ and $x=n+1.$ The positive value of $k$ that makes the following expression always true can be represented as $\frac{A}{B},$ for positive coprime $A$ and $B.$ Find $A+B.$ $\int_n^{n+k}f(x)\text{ }dx=\int_n^{n+k}l\text{ }dx$