You can utilize legacy Evaluate Macro function from Excel 4.0.
Set up:
1. Select Cell A2
2. Launch Name Manager and create new named range "SumCell"
3. Formula for the named range will be...
=EVALUATE(SUBSTITUTE(Sheet1!A$1,"/","+"))
4. In Cell A2 type =SumCell
Note: It is very important that you select Cell A2 when you create Named Range as column reference is left relative and will change as you copy formula across.
I assumed you had other values across row1 and needed formula to be somewhat dynamic.
Alternately you can do something like...
=SUM(IFERROR(VALUE(MID(A1,ROW($A$1:OFFSET($A$1,LEN(A1)-1,0)),1)),0))
Edit: Forgot to mention above formula must be confirmed as array (CTRL+SHIFT+ENTER)
However, this will only work with single digit integer values (i.e. it will not solve for 11/12/13 = 36, it will solve to 9).