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$a,b$ and $c$ are three positive real numbers such that $a+b+c=n$.

What is the smallest possible value of $n$ such that

$(ab+bc+ca)\left(\dfrac{a}{2b+3c}+\dfrac{b}{2c+3a}+\dfrac{c}{2a+3b}\right)\ge 20$

for all possible ordered triplets $(a,b,c)?$

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