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

• A. \(\dfrac{257}{16}\)
• B. \(\dfrac{256}{16}\)
• C. \(\dfrac{257}{15}\)
• D. \(\dfrac{265}{16}\)