Do you have ghostscript installed? CorelDraw can do a better job at importing PS and PDF files if it can use ghostscript to do it. Though that might not be the problem here.
Another possibility is that the font that you have installed locally may not be the exact font that was used to create the PDF. There could be differences in the character set, encoding or language settings.
In principle, you should have those apostrophes if you import as curves, and it should not matter whether you have the required font to do that. But when you import as editable, you need the exact same font to avoid seeing character mismatches.
When you installed X6, you had the opportunity to install ghostscript and may even have done it without knowing.
To check if you have it, go to windows control panel > programs and features. If you have it it will probably appear as GPL Ghostscript in the name column.
If you do not have it, you can either go to ghostscript.com or run a Coreldraw modify installation. Ghostscript.com will get you a newer version, but they both work well with CorelDraw.
Are you able to upload a small PDF that has the problem?