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#Mathematica, 51 bytes #
Total@ToExpression@StringCases[#,DigitCharacter..]&
Catching the wrong end of the verbose Mathematica builtins. 1 Byte off with the help of @DavidC
#Mathematica, 5251 bytes #
Total@ToExpression@StringSplit[#Total@ToExpression@StringCases[#,LetterCharacterDigitCharacter..]&
#Mathematica, 52 bytes #
Total@ToExpression@StringSplit[#,LetterCharacter..]&
Catching the wrong end of the verbose Mathematica builtins
