What is the area bounded by the curve \( y=x^6( \pi - x) ^8 \) between \( x=0 \) to \(x=\pi \) and \(x\)-axis?

The area can be represented as \( \dfrac{ \pi ^ab! c!}{d!} \), where \(a\), \(b\), \(c\), and \(d\) are positive integers. Find the value of \(a+b+c+d\).

\[\] **Notation:** \(!\) is the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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