Let \( f:\mathbb{R}\to\mathbb{R} \) be defined as \( f(x)=a e^{2x}+b e^{x}+c x \). If \( f(0)=-1 \), \( f'(\log_e 2)=21 \) and \(\displaystyle \int_{0}^{\log_e 4}\big(f(x)-c x\big)\,dx=\dfrac{39}{2} \), then the value of \( |a+b+c| \) equals.
\(10\)
\(8\)
\(12\)
\(16\)
