You need to add the [t]
positioning specifier not only to the minipage
environments, but to both tabular
environments as well.
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%% preamble stuff omitted\begin{longtable}{|A|B|} \fbox{ \begin{minipage}[t][6cm]{0.14\paperwidth} \begin{tabular}[t]{|p{0.12\paperwidth}|} % <--- "[t]" is new Left Table\\ left Table\\ \end{tabular} \end{minipage}}& \fbox{ \begin{minipage}[t][16cm]{0.69\paperwidth} \begin{tabular}[t]{|p{0.66\paperwidth}|} % <--- "[t]" is new Right Table\\ Right Table\\ Right Table\\ Right Table\\ Right Table\\ Right Table\\ Right Table\\ Right Table\\ Right Table\\ \end{tabular} \end{minipage}} \\\end{longtable}