\begin{document}$D\to P$\end{document} transition form factors within the framework of the light-cone QCD sum rules (LCSR) with the D-meson light-cone distribution amplitudes (LCDAs). The next-to-leading power (NLP) corrections to the vacuum-to-D-meson correlation function are considered, and the NLP corrections from the high-twist D-meson LCDAs and the SU(3) breaking effect from a strange quark mass are investigated. Adopting the exponential model of the D-meson LCDAs, the SU(3) flavor symmetry breaking effects are predicted as \begin{document}$R_{SU(3)}^{+,0}=1.12$\end{document} and \begin{document}$R_{SU(3)}^{T}=1.39$\end{document}, respectively, confirming the results obtained from LCSR with pion LCDA. The numerical predictions of the form factors show that the contribution from two-particle higher-twist contributions is of great importance and the uncertainties are dominated by the inverse moment of \begin{document}$\phi_D^+(\omega, \mu)$\end{document}. With the obtained form factors, the predicted Cabibbo-Kobayashi-Maskawa (CKM) matrix elements are \begin{document}$|V_{cd}|=0.151\,{}^{+0.091}_{-0.043} \big |_{\rm th.}\,{}^{+0.017}_{-0.02} \big |_{\rm exp.}$\end{document} and \begin{document}$|V_{cs}|=0.89\,{}^{+0.467}_{-0.234} \big |_{\rm th.}\,{}^{+0.008}_{-0.008} \big |_{\rm exp.}$\end{document}."> Higher-twist corrections to the <inline-formula><tex-math id="M1-1">\begin{document}${\boldsymbol{D\to\pi,K}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/1d8fd59d-29aa-4021-ab46-f67513922c70/CPC-2021-0333_M1-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/1d8fd59d-29aa-4021-ab46-f67513922c70/CPC-2021-0333_M1-1.png"/></alternatives></inline-formula> form factors from light-cone sum rules -
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