The polynomial \(P(x)=(1+x+x^2+\cdots+x^{17})^2-x^{17}\) has 34 complex roots of the form \(z_k = r_k[\cos(2\pi a_k)+i\sin(2\pi a_k)], k=1, 2, 3,\ldots, 34,\) with \(0 < a_1 \le a_2 \le a_3 \le \cdots \le a_{34} < 1\) and \(r_k>0.\) Given that \(a_1 + a_2 + a_3 + a_4 + a_5 = m/n,\) where \(m\) and \(n\) are relatively prime positive integers, find \(m+n.\)

(第二十二届AIME1 2004 第13题)