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已知集合 $A=\left\{x \mid x^2+2 x-8=0\right\}, B=\left\{x \mid x^2-5 x+6=0\right\}$, $C=\left\{x \mid x^2-m x+m^2-13=0\right\}$, 若 $B \cap C \neq \varnothing, A \cap C=\varnothing$, 则 $m=$
                        
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