The Degree Isn't Given Either?

Algebra Level 5

Let \(a_1, a_2, \ldots , a_n\) be the roots of the equation \(\displaystyle \sum_{k=1}^n kx^k = 0 \). If \( \displaystyle \sum_{k=1}^n \dfrac1{1-a_k} = 7 \), find \(n\).