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Default multiple if conditions - use sumif/sumProduct?

I have a situation where I need to sum a column based on several conditions
in different columns. For every "exp" item (column M), I must only sum
(column F) those that contain a "D" or "M" in column E. Below is the
forumula I used (and there was a sum product I used), but they either return
#VALUE or not the correct number. I've verified the data and used something
similar for just 1 argument and that has worked, but using more than 1 is
throwing me off. I may have to add more items from column E in the future,
so I need to know how to encompass more. Help!

=SUM(IF(($M1189:$M1316="exp")*($E1189:$E1316="D")+ ($E1189:$E1316="M"),$F1189:$F1316))