このエラーメッセージに関する原因と対処に関して説明します。
エラーメッセージ(英語)：
sdk permission denied
対処
関連リンク
Unable to install Homebrew ? Nicholas Workshop ? Medium
https://medium.com/nicholasworkshop/unable-to-install-homebrew-1c290a0f40d7
Recently Active 'permission-denied' Questions - Stack Overflow
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Highest Voted 'permission-denied' Questions - Stack Overflow
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macos - Mac OS X 10.11如何安装homebrew? - SegmentFault 思否
https://segmentfault.com/q/1010000002944716