If \(\dfrac{a}{b}=\dfrac{c^2}{d^2}=\dfrac{e^3}{f^3}=16,\) then find the value of \(\sqrt{\dfrac{a^2+c^4+e^6}{b^2+d^4+f^6}}+\sqrt{\dfrac{b^2+d^4+f^6}{a^2+c^4+e^6}}\).
1
\(\dfrac{257}{16}\)
2
\(\dfrac{256}{16}\)
3
\(\dfrac{257}{15}\)
4
\(\dfrac{265}{16}\)