Algebra Level 4

$$a, b, c, d$$ are distinct numbers such that:

• $$a$$ and $$b$$ are the roots of the equation $$x^2-2cx-5d=0$$
• $$c$$ and $$d$$ are the roots of the equation $$x^2-2ax-5b=0$$

Find the value of $$a+b+c+ d$$.

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