$$\(y=x^{p}+2 x^{q}\)$$ $$\[ \frac{\mathrm{d} y}{\mathrm{~d} x}=11 x^{10}+10 x^{4}, \text { where } \frac{\mathrm{d} y}{\mathrm{~d} x} \text { is the derived function. } \]$$ Find the value of $$\(p\)$$ and the value of $$\(q\)$$. $$\[ \begin{aligned} &p= ............................................ \\ &q= ............................................ \end{aligned} \]$$

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