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The full-heavy tetraquarks $cc\bar{c}\bar{b}$ and $bb\bar{b}\bar{c}$ are systematically investigated within the chiral quark model. The meson-meson structure, diquark-antidiquark structure and K-structure are considered in this work. There is no bound state for $cc\bar{c}\bar{b}$ and $bb\bar{b}\bar{c}$ systems in $ IJ^{P}=00^{+},01^{+}$ and $ 02^{+}$ channels. However, for $cc\bar{c}\bar{b}$ system, three possible resonance states with energy of $ 10079~{\rm MeV} $, $ 10081~{\rm MeV} $ and $ 10177~{\rm MeV} $ are found in $ IJ^{P}=00^{+},01^{+}$ and $ 02^{+}$, respectively, and their decay width $ Γ$ are $6.7-8.4~{\rm MeV} $, $1.4-7.2~{\rm MeV} $ and $9.1-11.1~{\rm MeV} $. For $bb\bar{b}\bar{c}$ system, there also exist three possible resonance states with energy of $ 16474~{\rm MeV} $, $ 16474~{\rm MeV} $ and $ 16541~{\rm MeV} $ in $ IJ^{P}=00^{+},01^{+}$ and $ 02^{+}$, respectively, and the decay widths $ Γ$ of them are $2.2-6.1~{\rm MeV} $, $2.2-6.9~{\rm MeV} $ and $5.3-8.5~{\rm MeV} $. $bc\bar{c}\bar{c}$ and $cb\bar{b}\bar{b}$ systems will have the same results as $cc\bar{c}\bar{b}$ and $bb\bar{b}\bar{c}$, respectively. These full-heavy resonance states are worthy to be searched in the future experiments.