  In this article, with the assumption of explicit isospin violation arising
from the $f_0(980)-a_0(980)$ mixing, we take the point of view that the scalar
mesons $f_0(980)$ and $a_0(980)$ have both strange and non-strange
quark-antiquark components and evaluate the strong coupling constants $g_{f_0
K^+ K^-}$ and $g_{a_0 K^+ K^-}$ within the framework of the light-cone QCD sum
rules approach. The large strong scalar-$KK$ couplings through both the
$n\bar{n}$ and $s\bar{s}$ components $g^{\bar{n}n}_{f_0 K^+ K^-}$,
$g^{\bar{s}s}_{f_0 K^+ K^-}$,
  $g^{\bar{n}n}_{a_0 K^+ K^-}$ and $g^{\bar{s}s}_{a_0 K^+ K^-}$will support the
hadronic dressing mechanism, furthermore, in spite of the constituent structure
differences between the $f_0(980)$ and $a_0(980)$ mesons, the strange
components have larger strong coupling constants with the $K^+K^-$ state than
the corresponding non-strange ones, $g_{f_0 K^+ K^-}^{\bar{s}s}\approx
\sqrt{2}g_{f_0 K^+ K^-}^{\bar{n}n}$ and $g_{a_0 K^+ K^-}^{\bar{s}s}\approx
\sqrt{2} g_{a_0 K^+ K^-}^{\bar{n}n}$. From the existing controversial values,
we can not reach a general consensus on the strong coupling constants $g_{f_0
K^+ K^-}$, $g_{a_0 K^+ K^-}$ and the mixing angles.
