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Why does \textstyle not work in \smashoperator?

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In the following code, the \sum in \smashoperator appears too big. But if I put \textstyle\sum in \smashoperator, then it gives the error "*.tex: error: 290: Limit controls must follow a math operator. ...extstyle\sum_{\alpha\in D_{1}\cup D_{2}}}". I don't know what to do and need help. The MWE LaTeX code is as below:

\documentclass[11pt,twoside]{article}%\usepackage{amssymb}\usepackage{amsmath}\usepackage{amsfonts}\usepackage{mathtools}\usepackage[title,titletoc,header]{appendix}\usepackage{geometry}\usepackage{graphicx}\usepackage{indentfirst}\usepackage{mathrsfs}\usepackage{nopageno}\usepackage{setspace}\usepackage{remreset}\newtheorem{theorem}{Theorem}[section]\newtheorem{definition}[theorem]{Definition}\begin{document}\begin{enumerate}\item $\smashoperator{\sum_{\alpha\in D_{1}\cup D_{2}}}\,x_{\alpha}\,=\underset{\alpha\in D_{1}}{\textstyle\sum}x_{\alpha} \,+\underset{\alpha\in D_{2}}{\textstyle\sum}x_{\alpha}$\end{enumerate}\end{document}

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