Rotating digits of a three digit number.

Let us consider a three digit number \(\overline{a b c}\).

If 9 is added to this number, it becomes \(\overline{a c b}\), and let this be called ‘new number’.

If 90 is added to the ‘new number’, it becomes \(\overline{c a b}\).

What is the sum of the largest possible number and the smallest possible number of this type?

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