John ordered \(4\) pairs of black socks and some additional pairs of blue socks. The price of the black socks per pair was twice that of the blue. When the order was filled, it was found that the number of pairs of the two colors had been interchanged. This increased the bill by \(50\)%. The ratio of the number of the pairs of black socks to the number of pairs of blue socks in the original order can be expressed as \(a:b\) in the simplified form. Find \(a+b\).

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