A number theory problem by Paola Ramírez

\[\begin{cases} A=2 \\ C=AB \\ D=BC \\ E=CD \\ F= DE \\ F=6075000 \end{cases}\]

Given that six positive integers \(A,B,C,D,E\) and \(F\) meet the conditions above, find the value of \(B+C+D+E\).

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