Frank mistakenly believes that the number $1011$ is prime and for some integer $x$ writes down:
\[
(x+1)^{1011} \equiv x^{1011} + 1 \pmod{1011}.
\]
However, it turns out that for Frank's choice of $x$, this statement is actually true. If $x$ is positive and less than $1011$, what is the sum of the possible values of $x$?

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