Dancers all over

Algebra Level 2

There are 3 dancers, Bingo,Mingo\color{#D61F06}{\text{Bingo}} ,\color{#3D99F6}{\text{Mingo}} and Tingo\color{#20A900}{\text{Tingo}} .

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

Bingo::::y=x352x+96\color{#D61F06}{\text{Bingo}} :::: \color{#D61F06}{y =x^3-52x+96 }

Mingo::::y=x+44\color{#3D99F6}{\text{Mingo}} :::: \color{#3D99F6}{y= x+44}

Tingo::::y=x424x3+148x2336x+256\color{#20A900}{\text{Tingo}} :::: \color{#20A900}{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)(a,b) in Cartesian system, and aa and bb are integers . Find the value of a+b\color{#69047E}{a+b}

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