Ain't it Infinite?!

Algebra Level 4

a,b,c,d,eR+a,b,c,d,e \in \mathbb{R^+}, and follow a+b+c+d+e=40a+b+c+d+e=40 and ab+ac+ad+ae+bc+bd+be+cd+ce+de=640ab+ac+ad+ae+bc+bd+be+cd+ce+de=640 simultaneously. Determine the SUM of ALL possible values of "a".

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