Algebra Level pending

Let $$Ax^4 + Bx^3 + Cx^2 + Dx + E= 0$$ be an equation with integer coefficients such that $$A$$ is positive, $$\gcd(A,B,C,D,E) = 1$$, and the roots are $$\sqrt2,-\sqrt2,\sqrt3,-\sqrt3$$.

Find $$A+B+C+D+E$$.

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