If $ab \neq 0$ and $|a| \neq |b|$, find the number of distinct values of $x$ satisfying the equation
\[ \frac{x-a}{b} + \frac{x-b}{a} = \frac{b}{x-a} + \frac{a}{x-b} \].

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