Making the assumption of explicit isospin violation arising from 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 $g_{f_0 K^+ K^-} \;\mathrm{and}\; g_{a_0 K^+ K^-}$ 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 cannot reach a general consensus on the strong coupling constants $g_{f_0 K^+ K^-} , g_{a_0 K^+ K^-}$ and the mixing angles.