Parabola Problem

Algebra Level 3

A parabola passes through the following points

\[ \left( -1,1 \right) ,\left( 0,0 \right) ,\left( \dfrac { 1 }{ 2 } ,\dfrac { 1 }{ 4 } \right) ,\left( 1,1 \right) ,\left( -\dfrac { 7 }{ 5 } ,-\dfrac { 3 }{ 5 } \right). \]

It also passes through the point: \((\dfrac { 289 }{ 240 } ,\dfrac { a }{ b } ),\) where \(a,b\) are positive coprime integers. Find \(a+b\)

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