What is the minimum value of \((x^2+2x+8-4\sqrt{3})\cdot(x^2-6x+16-4\sqrt{3})\) where \(x\) is a real number? The answer should be in the form \(a - b\sqrt{3}\). Please find the value of \(a + b\).

Let's think step by step and output the final answer within \boxed{}.
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