A Complex Problem

Algebra Level 5

Let $a, b, c$ be 3 complex numbers such that $|a| = |b| = |c| = 1$ and $\dfrac{a^2}{bc}+ \dfrac{b^2}{ac} + \dfrac{c^2}{ab} + 1 = 0$ . If $|a + b + c|$ can take values that equal $p$ and $q$ , then find the value of $p+q$ .