Adding up the digits and the digits reversed

05AB1E, 7 bytes

LDRJsJ+

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Explanation

LDRJsJ+

L        range from 1 .. input
 D       duplicate
  R      reverse
   JsJ   convert both arrays to strings
      +  add (coerces both strings to ints)

Jelly, 9 bytes

R,U$DF€ḌS

 

CJam, 15 14 bytes

Thanks to Martin for shaving a byte!

ri,:)_W%si\si+

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