Number sum divisibility

Adam wrote the following sum with five secret adders:
a + bb + ccc + dddd + eeeee.

He revealed that the characters "a, b, c, d, e" represent the different digits 1, 2, 3, 4, and 5 and that the resulting sum is divisible by 11.
Which is the smallest and which is the largest number that can result from Adam's sum?

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