The LEO page for "Sinne" shows that the noun Sinne is a feminine noun, yet is used in the phrase "in diesem Sinne".
Shouldn't that be "in dieser Sinne"?
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I'm sure this is a misunderstanding.
The "-e"-ending appears to be a relict from times when German still formed the Dative with a suffix. It's retained in phrases like "im Jahre xxxx", in quotations like "dem Manne kann geholfen werden". Perfectly correct, if not extremely common.
Secondly: Where does it say feminine on the LEO page?
Edit: Em1 pointed out the possible reason for the confusion... remember: the article "die" is used for the plural of all nouns, regardless of their gender.
Your confusion is effected through the plural form: der Sinn, die Sinne.
In diesem Sinne is only one Sinn, not many Sinne.
The dative of der Sinn is built up with dem and not der as in feminine nouns.
So it is correct to say In diesem Sinne.
(Regarding the -e take notice of Mac's answer)