Let \( f(x) = x^4 - 6x^3 + 26x^2 - 46x + 65 \).
Let the roots of \( f(x) \) be \( a_k + ib_k \) for \( k = 1, 2, 3, 4 \).
Given that the \( a_k \), \( b_k \) are all integers, find \( |b_1| + |b_2| + |b_3| + |b_4| \).

Let's think step by step and output the final answer within \boxed{}.
user