Calculate the sum of ILD

Python 2, 39 bytes

lambda x:x+len(`x`)+eval("+".join(`x`))

Test suite

Using the same eval-trick as in my Pyth-answer.

05AB1E, 28 20 18 8 bytes

ÐgsS'+ýO

Explanation

Ð           # triplicate input
 g          # get length of input
  sS'+ý     # split input and merge with '+' as separator 
       O    # sum and implicitly display

Try it online

Saved 10 bytes thanks to @Adnan

Pyth, 11 10 bytes

Thanks to @LeakyNun for a byte!

++vj\+`Ql`

Test suite

Explanation

++vj\+`Ql`QQ  # Q = input, last two implicitly added

  vj\+`Q      # Join the input on '+' and eval it
        l`Q   # Length of the input
           Q  # The input itself
++            # Add those three values to obtain the result