There are 3 dancers, \(\color{Red}{\text{Bingo}} ,\color{Blue}{\text{Mingo}}\) and \(\color{Green}{\text{Tingo}}\) .

They are dancing, and during their dance, they move along the path in the Cartesian plane as stated below.

\(\color{Red}{\text{Bingo}} :::: \color{Red}{y =x^3-52x+96 }\)

\(\color{Blue}{\text{Mingo}} :::: \color{Blue}{y= x+44}\)

\(\color{Green}{\text{Tingo}} :::: \color{Green}{y =x^4 - 24x^3 + 148x^2 - 336x + 256}\)

They all yell out "WOW" if they all meet at a point.

The point where they yell "WOW" can be stated as \((a,b)\) in Cartesian system, and \(a\) and \(b\) are integers . Find the value of \(\color{Purple}{a+b}\)

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