Find the value

Algebra Level 4

Assuming that \( ab+ac+bc=2014 \) and \( a \neq b \neq c \),

Evaluate: \( \dfrac { { a }^{ 3 }(b+c) }{ (a-b)(a-c) } +\dfrac { { b }^{ 3 }(a+c) }{ (b-a)(b-c) } +\dfrac { { c }^{ 3 }(b+a) }{ (c-b)(c-a) } \)

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