##Seriously, 13 bytes

,ú;û+@s`≈`MΣl

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Explanation:

,ú;û+@s`≈`MΣl
,              push input
 ú;û+          push "abc...zABC...Z" (uppercase and lowercase English letters)
     @s        split on letters
       `≈`M    convert to ints
           Σ   sum
            l  length (does nothing to an integer, pushes 0 if an empty list is left, in the case where the string is all letters)

Seriously, 13 bytes

,ú;û+@s`≈`MΣl

Try it online!

Explanation:

,ú;û+@s`≈`MΣl
,              push input
 ú;û+          push "abc...zABC...Z" (uppercase and lowercase English letters)
     @s        split on letters
       `≈`M    convert to ints
           Σ   sum
            l  length (does nothing to an integer, pushes 0 if an empty list is left, in the case where the string is all letters)

##Seriously, 12 bytes

,ú;û+@s`≈`MΣ

Try it online!

Explanation:

,ú;û+@s`≈`MΣ
,             push input
 ú;û+         push "abc...zABC...Z" (uppercase and lowercase English letters)
     @s       split on letters
       `≈`M   convert to ints
           Σ  sum

##Seriously, 13 bytes

,ú;û+@s`≈`MΣl

Try it online!

Explanation:

,ú;û+@s`≈`MΣl
,              push input
 ú;û+          push "abc...zABC...Z" (uppercase and lowercase English letters)
     @s        split on letters
       `≈`M    convert to ints
           Σ   sum
            l  length (does nothing to an integer, pushes 0 if an empty list is left, in the case where the string is all letters)