Given
\[ \large \overline{QQ.Q}+\overline{QQ.Q}=\overline{RRR.T}\]
Where \(Q,R,T\) are single digit non-negative integers, with
\(Q\) is an odd prime number,
\(R\) is a number that slashes through everything (metaphor), and
\(T\) is nothing (another metaphor).
What is the value of \(Q+R+T\)?
Details and assumptions
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